In [1]} it has been shown that the \(\kappa \) -sum is substantially equivalent to the relativistic addition of momenta and there it was conjectured a possible relation between the \(\kappa \) -statistics and the theory of the special relativity. In this sense, the \(\kappa \)  parameter plays the role of a speed limit according to the relation \(\kappa \propto 1/c\) . Consequently, in the \(\kappa \rightarrow 0\)  limit, corresponding to the Galilean relativistic limit (\(c\rightarrow \infty \) ), the \(\kappa \) -sum reduces to the standard sum and consistently, the arcsinh-normal distribution (REF ) recovers the Gaussian distribution that, as stated by the standard central limit theorem, is the stable limiting distribution of the sum of iid random variables.
